In this paper, we propose a new class of local differential privacy (LDP) schemes based on combinatorial block designs for discrete distribution estimation. This class not only recovers many known LDP schemes in a unified framework of combinatorial block design, but also suggests a novel way of finding new schemes achieving the exactly optimal (or near-optimal) privacy-utility trade-off with lower communication costs.

Successful training of data-intensive deep neural networks critically rely on vast, clean, and high-quality datasets. In practice however, their reliability diminishes, particularly with noisy, outlier-corrupted data samples encountered in testing. This challenge intensifies when dealing with anonymized, heterogeneous data sets stored across geographically distinct locations due to, e.g., privacy concerns. This present paper introduces robust learning frameworks tailored for centralized and federated learning scenarios.

We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian (location) problem. Most existing bounds are order-wise loose in this setting, which has raised concerns about the fundamental capability of information-theoretic bounds in reasoning the generalization behavior for machine learning. The proposed new bound adopts the individual-sample-based approach proposed by Bu et al., but also has several key new ingredients.

The sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs). In the existing literature on CBs, a critical assumption is that the causal models remain constant over time. However, this assumption does not necessarily hold in complex systems, which constantly undergo temporal model fluctuations. This paper addresses the robustness of CBs to such model fluctuations. The focus is on causal systems with linear structural equation models (SEMs).

We present a computationally efficient framework, called FlowDRO, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from it. The requirement for LFD to be continuous is so that the algorithm can be scalable to problems with larger sample sizes and achieve better generalization capability for the induced robust algorithms.

In many real-world problems, predictions are leveraged to monitor and control cyber-physical systems, demanding guarantees on the satisfaction of reliability and safety requirements. However, predictions are inherently uncertain, and managing prediction uncertainty presents significant challenges in environments characterized by complex dynamics and forking trajectories. In this work, we assume access to a pre-designed probabilistic implicit or explicit sequence model, which may have been obtained using model-based or model-free methods.

We consider the problem of continually releasing an estimate of the population mean of a stream of samples that is user-level differentially private (DP). At each time instant, a user contributes a sample, and the users can arrive in arbitrary order. Until now these requirements of continual release and user-level privacy were considered in isolation. But, in practice, both these requirements come together as the users often contribute data repeatedly and multiple queries are made.

We study the distributed mean estimation (DME) problem under privacy and communication constraints in the local differential privacy (LDP) and multi-message shuffled (MMS) privacy frameworks. The DME has wide applications in both federated learning and analytics. We propose a communication-efficient and differentially private algorithm for DME of bounded $\ell _{2}$ -norm and $\ell _{\infty }$ -norm vectors. We analyze our proposed DME schemes showing that our algorithms have order-optimal privacy-communication-performance trade-offs.